Sheet material cutting device and cutting block therefor

ABSTRACT

A sheet material cutting device which includes a cutting board and a guide extending over the top of the board. A cutting block is mounted for sliding movement along the guide. The cutting block may include a base and a cutting blade normally biased away from the board, but adapted to be pivoted toward the board into engagement with a sheet positioned thereon. Where bevel cuts are desired, the cutting blade is at a non-perpendicular angle to the cutting board and the cutting blade is pivoted into angular engagement with the sheet. A scale is mounted for movement with the cutting block. The scale has a reference marking at the point where the cutting blade engages a sheet and extends from the reference point in at least one direction. The scale may be utilized to easily and accurately determine points at which the beginning and end of a cut occur.

United States Patent [1 1 Matthew Nov. 27, 1973 SHEET MATERIAL CUTTINGDEVICE AND Primary ExaminerWillie G. Abercrombie CUTTING BLOCK THEREFORAtt0rneyRonald J. Kransdorf [76] Inventor: Morton Pomeroy Matthew,Kreiner LIL, Norwalk, Conn. 06850 57 ABSTRACT [22] Filed: Jan. 28, 1972[52] US. Cl 83/522, 83/468, 83/581, 83/564, 83/614, 83/638 [51] Int. Cl.B26d 7/28 [58] Field of Search 83/522, 581, 563, 83/564, 614, 620, 638,468

[56] References Cited UNITED STATES PATENTS 3,527,131 9/1970 Ellerin etal. 83/522 3,668,956 6/1972 Whipple et al. 83/522 X 3,463,041 8/1969Shapiro et a1 83/614 X 570,180 10/1896 McCall 83/581 A sheet materialcutting device which includes a cutting board and a guide extending overthe top of the board. A cutting block is mounted for sliding movementalong the guide. The cutting block may include a base and a cuttingblade normally biased away from the board, but adapted to be pivotedtoward the board into engagement with a sheet positioned thereon. Wherebevel cuts are desired, the cutting blade is at a non-perpendicularangle to the cutting board and the cutting blade is pivoted into angularengagement with the sheet. A scale is mounted for movement with thecutting block. The scale has a reference marking at the point where thecutting blade engages a sheet and extends from the reference point in atleast one direction. The scale may be utilized to easily and accuratelydetermine points at which the beginning and end of a cut occur.

19 Claims, 6 Drawing Figures PATENTEDNUV 21 3,774,4 sum as; 2

SHEET MATERIAL CUTTING DEVICE AND CUTTING BLOCK THEREFOR This inventionrelates to a device for cutting sheet material such as cardboard orpaper and more particularly to a cutting block for such a device.

BACKGROUND OF THE INVENTION US. Pat. No. 2,803,303 entitled PaperCutting Device and Board Therefore, issued Aug. 20, 1957 .to Morton P.Matthew, shows a device for makingstraight cuts in soft sheet materialssuch as cardboard or paper.

This device consists of a cutting boardhaving anelongatedguideresiliently supported upon the top thereof.

A cutting block is mounted for sliding movement along the guide and-hasabladeprojecting therefrom which is moved into engagement with a sheeton the board whenthe guide isrlowered toward the board. A scale isprovided along' the board whichis indexed on the end of the .block toindicate the'length of a out.

While the relatively simple device described above is adequatefor manypurposes, there are various ways in which it can be improved'or modifiedto perform a sired to, for example, make a out which begins one inchfrom a first edge of a sheet and ends one inch from the opposite edge ofthe sheet with the device indicated above, one must initially measureand mark the positions on the sheet at which the cuts are to begin andend before placing the sheet on the board for cutting. Even with themarks, it is difficult to see the position of the blade on the sheet,and extreme care must be used in making a cut to avoid overcutting.

The device of the above-mentioned Matthew patent could thus be improvedby providing .a means on the device for indicating the exact position ofthe blade on the sheet relative to an edge of the sheet or some otherpredetermined point. Such a device should be simple to use and shouldalso be simple in design so as to be relatively easy and inexpensive toadd to the device.

The problem of making accurate cuts which begin and end atpredeterminedpositions of a sheet arises particularly when the device isbeing utilized to cut display windows in mats of the type utilized tomount pictures and the like. Heretofore, the cutting of mats has Inormally involved an initial measuring and marking either on the frontor back of the mat. Since a shear can not be used to make suchapertures, a knife or other blade must be utilized. However, it requiresskillful I knife manipulation to reproduce an unwavering cut withaccurate terminations. The problem is compounded by the fact that bevelcuts are normally utilized for mats, requiring the blade to be held at aprecise angle. To ease these difficulties, some mechanical mat cuttershave been developed. However, these cutters have normally beenrelatively complicated and expensive and have generally still requiredan initial measuring and marking of the mat.

A need therefore exists for a relatively simple and inexpensive devicefor making bevel cuts in a mat without the need for initial measuringand marking. In order for the device of the Matthew patent to fulfillthese requirements, its cutting block must be modified, or a new cuttingblock provided, so as to enable the device to make bevel cuts. At firstglance it would appear that the conversion from a straight cutter to abevel cutter could be made by merely mounting the blade in the cuttingblock of the Matthew patent at the desired angle. However, an attempt tomove an angled blade directly into a sheet or mat, as is done with thestraight blade in the Matthew patent, could cause the blade to bend orbreak. The cutting block must thus be modified to permit the blade to bebrought into the mat at an angle rather than straight down. In order topermit proper meeting at comers, it is preferable that this angle'beselected so as to be equal to the bevel angle.

Aprimary object of this'invention is thus to provide an improved sheetmaterial cutting device.

A'more specific object of this invention is to provide a sheet materialcutting device whichpermits a position on the sheet'or mat at which acut begins and/or ends to be quickly, easily, directly, and accuratelydetermined, eliminating the need =for premeasuring and marking a sheetand premitting cuts to be made from the-front of the sheet.

Another object of this invention is to provide a sheet material cuttingdevice adapted for making bevel cuts.

A further object of this invention is to provide a relatively simple andinexpensive device for quickly, easily, and accurately cutting mats.

SUMMARY OF THE INVENTION In accordance with these objects, thisinvention provides a sheet material cutting device which includes acutting board and a guide extending over the top of the board. A cuttingblock is mounted for sliding movement along the guide. The cutting blockmay include a base and a cutting means normally biased away from theboard, but adapted to be pivoted toward the board into engagement with asheet positioned thereon. Where'bevel cuts are desired, the cuttingmeans is at a non-perpendicular angle to the cutting board and thecutting means is pivoted into angular engagement with the sheet. A scaleis mounted for movement with the cutting block. The scale has areference marking at the point where the cutting means engages a sheetand extends from the reference point in at least one direction. Thescale may be utilized to easily and accurately determine points at whichthe beginning and end of a cut occur.

The foregoing and other objects, features, and advantages of theinvention will be apparent from the following more detailed descriptionof a preferred embodiment of the invention as illustrated in theaccompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS FIG. 1 is a top view of a sheet materialcutting device of a preferred embodiment of the invention, showing thedevice at the beginning of a cut.

FIG. 2 is a top view of the cutting device shown in FIG. 1 showing thedevice at the end of a cut.

FIG. 3 is a top view of a cutting block suitable for use for makingbevel cuts with a device of the type shown in FIGS. 1 and 2.

FIG. 4 is a left side view of the cutting block shown in FIG. 3.

FIG. 5 is a rear view of the cutting block shown in FIGS. 3 and 4.

FIG. 6 is a plain view of a typical work piece after performing thecutting operations for fabricating a picture mat.

DETAILED DESCRIPTION 7 Referring now to FIG. 1, a cutting device of thegeneral type shown in the beforementioned Matthew U.S. Pat. No.2,803,303 is shown. The device consists of a board 10 which may be ofwood, but is preferably of a softer material, such as soft compositionboard so as to be adapted to receive a pin or staple. Two scalesections, 12 and 14, are mounted along the upper edge of board 10 byscrews 16. As in the Matthew patent, the scale sections are slightlyspaced from board 10 so as to permit a disposable, board protectingsheet to be fitted under the scales and held thereby. Plate 17, whichmay be in two separate sections, is mounted on top of scales 12 and 14and secured thereto by the screws 16. A leaf spring 20, normally biasedaway from board 10, is mounted to plate 17 by rivets 22 or othersuitable means and has secured to its underside, by rivets or similarmeans 24, an elongated metal guide rail 26. Guide rail 26 extends alongthe top of board 10 at an angle perpendicular to that of scales 12 and14. A bracket 28 is mounted on an arm 29 fixed to board 10 and ispositioned under the end of rail 26 opposite leaf spring 20. Thefunctions of this bracket will be described later. i

A cutting block 30, having a scale 32 and a cutting blade 34 supportedthereon, is mounted for sliding movement along rail 26. Cutting block 30is shown in greater detail in FIGS. 3-5. Referring now to those figures,it is seen that cutting block 30 consists of a base 36 which has a guiderail receiving groove 38 (see FIG. 5) in its underside and aperpendicular flange 40. A blade holder 42 is pivotably secured by pin44 to flange 40. As may be best seen in FIG. 5, blade holder 42 ismounted at an angle to the perpendicular which angle is, for thepreferred embodiment of the invention, 60. A screw 46, the head of whichis of sufficient size to be easily finger operable, secured blade 34,which may be a standard utility knife blade, to holder 42. A trough 48formed in blade holder 42 aids screw 46 in holding the blade inposition. A cantilever spring 50 mounted in a groove 52 in blade holder42 normally coacts with base 36 to bias the blade holder, and thus blade34, counterclockwise. Blade holder 42 is thus normally in a raisedposition bringing the tip of blade 34 into a recessed position behindscale 32. Blade holder 42 also has a pad 54 secured to or, for apreferred embodiment of the invention, formed into its leading face.Pressure applied to pad 54 as by, for example, a persons thumb rotatesblade holder 42 clockwise about pin 44 to lower the blade into theposition shown in FIGS. 3-5. Continued pressure applied to pad 54 afterthe blade has been lowered causes cutting block 30 to move on rail 26 inthe direction the pressure is applied (upward as viewed in FIG. 1). Aset screw 55 in pad 54 may be adjusted to control the depth of cut in amat 18. The screw, when screwed in, bears against base 36 to limit thedownward movement of holder 42 and thus decrease the depth of cut.

Scale 32 secured to base 36 by screws 56 serves two important functions.First, scale 32 is mounted so that it stands off slightly from base 36to form a close fitting slot with the base through which blade 34passes. Since the width of this slot is just slightly greater than thethickness of the blade, the bladeis held against lateral movements onboth sides. This prevents shimmying of the blade and provides a straightcut. Scale 32 also, in a manner to be now described, permits thestarting and ending position of a cut to be accurately determined.However before describing the operation of the device, three additionalfeatures of scale 32 should be noted. First scale 32 has two zeromarkings which are slightly displaced from each other. From the figures,it is seen that this displacement is roughly equal to the width of theblade which projects beyond the scale. The double zero markings are thuseffective to compensate for the width of the blade. Second, scallop 58is provided between the two zero markings to provide maximum visabilityof the blade. Finally, the forward or left-hand portion of scale 32 notadjacent block 30 is raised slightly to permit this scale to clear scale12, leaf spring 20 and plate 17 when the block is, for example, in theposition shown in FIG. 2. Similarly, the portions of scales l2 and 14adjacent guide rail 26 are cut back slightly to provide clearance forblock 30 when a cut is made to the top of the mat.

OPERATION In operation, a mat 18 is initially positioned on board 10 byuse of scales 12 and 14. Thus, as shown in FIG. 1, mat 18 is positionedso that the first cut is made along a line which is two inches from theright edge of the mat and/or seven inches from the left edge of the mat.Scales 12 and 14 permit the position of the cut line to be preciselydetermined relative to either edge of the mat. Scale 14 may be dispensedwith if mat positioning is to be done only along the left edge of themat.

When the mat has been properly positioned on board 10, guide rail 26 ismoved down against the action of spring 20 into engagement with bracket28. Bracket 28 serves to maintain the long cantilevered guide rail 26perpendicular to scales l2 and 14, preventing lateral motion thereofcaused by side pressures occurring clur' ing cutting. This assures astraight perpendicular cut. Bracket 28 being mounted on arm 29 permits along mat 18 to pass between the bracket and board 10. Where mats longerthan rail 26 are not to be cut, bracket 28 may be mounted directly underthe rail.

Rail 26 having the cross section shown in FIG. 5, being thicker in themiddle then the thickness of cutting block base 36, the bottom edge ofthe rail can be permitted to come to rest on the mat. The rail assuresuniform spacing of the block from the mat and holds the block slightlyabove the mat so that the block moving over the mat does not mar it.

The next step in the operation is to position blade 34 for the beginningof the desired cut. In FIG. 1, it is assumed that the cut is to beginone inch from the lower edge of the mat. FIG. 1 illustrates how scale 32is utilized to properly position blade 34 to begin this cut, beingindexed on the lower edge of the mat for this purpose. When the scale 32indicates that blade 34 is properly positioned to initiate the cut, theoperator presses down on pad 54, preferably with his thumb, to rotateblade holder 42 clockwise about pivot 44 against the action of spring50. This rotation moves blade 34 to the position shown in FIGS 3-5,causing the blade to enter mat 18 at the desired point. Since blade 34is pivoted into contact with mat 18 rather than being pushed down intoit, the blade enters the mat at an angle. For

reasons which will be described shortly, this angle should be the sameas the angle at which the cut is beveled. For the embodiment of theinvention shown in the figures, this angle is 60. The angle at which theblade enters the mat is established by the proper location of pivot 44with respect to blade 34.

After the blade 34 has been rotated into contact with mat 18, continuedpressure on pad 54 is effective to move block 30 upward as shown inFIGS. 1 and 2 along rail 26. Since blade 34 is in the mat at this time,a cut is made in the mat as block 30 moves along the mat. It should benoted that the three aforementioned steps, namely: 1. moving guide rail26 downward, 2. rotating holder 42 and blade 34 clockwise, and 3. movingblock 36 to cut, are easily and sequentially performed using only theindex finger and thumb of one hand applied to 36 and 54 respectively.

FIG. 2 illustrates the manner in which scale 32 is utilized to easilyand accurately determine the endpoint for the cut. Assume that the cutis to terminate one inch from the top edge of mat 18. Block 30 is thusmoved along rail 26 until scale 32 indicates that blade 34 is exactlyone inch from the top of the mat. This is the position shown in FIG. 2,with scale 32 being indexed on the top of the mat. When this position isreached, pressure is released from pad 54, permitting blade 34 to beremoved from the mat by the action of spring 50 on blade holder 42. Afirst bevel cut of the type'shown in FIG. 6 is in this manner effected.

For the second cut, the mat is again positioned on board by use ofscales l2 and 14. Rail 26 is again lowered into operative position andblade 34 positioned to the beginning of the cut by use of scale 32. Ifit is assumed that the first cut in mat 18 is the cut 62 shown in FIG.6, and that the second cut to be made is the cut 64, it can be seen thatbecause of the selected angle for the bevel, the comer 66 at which thecut would begin for cut 64 is at a a 60 angle. Thus, the blade enteringthe mat at this angle prevents the blade from causing any overcut orother damage to the mat when the blade enters. Clean corners are thusassured. The sequence of operations described above would be repeatedfor cutting the two remaining sides of the opening shown in FIG. 6.

A supplementary cutting block may be used in place of block 30, with afixed perpendicular blade, similar to that covered in the beforementioned Matthew patent, so that the present invention may be used tocut the outline of the mat to size before bevel cutting the inside.Either or both of these cutting blocks can function on the rail 26without lips or other means reaching around and under the rail so thatone block may be quickly lifted off the rail and exchanged with anotherblock.

A relatively simple and inexpensive cutting device has thus beenprovided which permits the start and end points for a cut in a piece ofsheet material to be quickly, easily, and accurately determined withoutrequiring any premeasuring or premarking of the sheet or mat. A uniquemat cutting structure utilizing the teachings of this invention has alsobeen disclosed. In addition to the various possible modificationsmentioned previously, it is apparent that additional modifications inthe specific elements utilized for performing the various functionsdescribed above could be made by one ordinarily skilled in the art whilestill remaining within the teachings of the invention.

What is claimed is:

l. A cutting block for a sheet material cutting device, said devicehaving a cutting board and a guide extending over the top of the boardcomprising:

a base mounted for sliding movement along said guide;

a cutting means pivotally supported on said base, said cutting meansbeing normally biased away from said board, but being adapted forpivoting toward the board to engage a sheet positioned thereon; and

a scale mounted for movement with said base, said scale having areference marking at the point where said cutting means engages a sheetwhen pivoted and extending from said reference marking in at least onedirection, said scale being graduated in units of linear measurementstarting at said reference marking and being adapted to be directlyindexed on an edge of said sheet material, whereby the points at whichthe beginning and end of a cut occur may be easily and accuratelyobserved.

2. A cutting block of the type described in claim 1 wherein said cuttingmeans includes a blade holder having a blade supporting face, means forclamping a cutting blade to said face, and a part to which pressure maybe applied to pivot said cutting means.

3. A cutting block of the type described in claim 2 wherein said part towhich pressure may be applied is positioned so that pressure applied tosaid part after the cutting means has engaged a sheet is operative tomove the block along the guide in the direction of the pressure.

4. A cutting block of the type described in claim 2 wherein said bladesupporting face is at a nonperpendicular angle to said board wherebysaid cutting means makes bevel cuts in a sheet.

5. A cutting block of the type described in claim 4 wherein the pivotingof said cutting means causes it to engage a sheet at an angle; and

wherein the angle at which said cutting means engages a sheet is equalto said non-perpendicular angle.

6. A cutting block of the type described in claim 5 wherein saidnon-perpendicular angle is 60.

7. A cutting block of the type described in claim 2 wherein said scaleis positioned parallel to said blade supporting face and is spacedtherefrom by a distance slightly greater than the thickness of a cuttingblade, whereby a blade positioned between the face and the scale is heldagainst lateral movement.

8. A cutting block of the type described in claim 1 wherein said cuttingmeans is supported at a nonperpendicular angle to said board wherebybevel cuts may be made in a sheet.

9. A cutting block of the type described in claim ll wherein said scaleextends in both directions from said reference marking.

10. A cutting block of the type described in claim 9 wherein there are apair of said reference markings, one for each direction in which saidscale extends, said reference markings being slightly separated tocompensate for the width of the blade.

111. A cutting block of the type described in claim 1 including at leastone scallop in said scale in the area of said reference marking toprovide maximum visibility of the blade in that area.

12. A sheet material cutting device comprising:

a cutting board;

a guide extending over the top of the board;

a cutting block mounted for sliding movement along said guide, saidcutting block including a cutting means normally biased away from saidboard but adapted to be moved toward the board into engagement with asheet position thereon; and

a scale mounted for movement with said block, said scale having areference marking at the point where said cutting means engages a sheetand extending from said reference marking in at least one direction,said scale being graduated in units of linear measurement starting atsaid reference marking and being adapted to be directly indexed on anedge of said sheet material, whereby the points at which the beginningand end of a cut occur may be easily and accurately observed.

13. A device of the type described in claim 12 wherein said scaleextends in both directions from said reference marking.

14. A device of the type described in claim 12 including a stationaryscale positioned on top of said board and extending from near one end ofsaid guide in a direction perpendicular thereto.

15. A device of the type described in claim 14 wherein said stationaryscale extends in both directions from said guide.

16. A device of the type described in claim 12 including means forsupporting said guide to prevent lateral movement thereof.

17. A device of the type described in claim l6 wherein said means forsupporting is a bracket mounted to permit a large sheet to passthereunder.

18. A mat cutting device comprising:

a cutting board adapted to have a mat positioned thereon;

a guide extending over the top of the board;

a cutting block mounted for sliding movement along said guide, saidcutting block including a cutting means mounted at a non-perpendicularangle to the board, said cutting means being normally biased away fromsaid board but being adapted to be pivoted into angular engagement witha mat position on said board and to be moved with said block along saidguide to make a bevel cut in said mat; and

a scale mounted for movement with said block, said scale having areference marking at the point where said cutting means engages a matwhen pivoted and extending from said reference marking in at least onedirection, said scale being graduated in units of linear measurementstarting at said reference marking and being adapted to be directlyindexed on an edge of said sheet material, whereby the points at whichthe beginning and'end of a cut occur may be easily and accuratelyobserved.

19. A mat cutting device of the type described in claim 18 wherein theangle at which said cutting means is pivoted into engagement with saidmat is equal to said non-perpendicular angle.

1. A cutting block for a sheet material cutting device, said devicehaving a cutting board and a guide extending over the top of the boardcomprising: a base mounted for sliding movement along said guide; acutting means pivotally supported on said base, said cutting means beingnormally biased away from said board, but being adapted for pivotingtoward the board to engage a sheet positioned thereon; and a scalemounted for movement with said base, said scale having a referencemarking at the point where said cutting means engages a sheet whenpivoted and extending from said reference marking in at least onedirection, said scale being graduated in units of linear measurementstarting at said reference marking and being adapted to be directlyindexed on an edge of said sheet material, whereby the points at whichthe beginning and end of a cut occur may be easily and accuratelyobserved.
 2. A cutting block of the type described in claim 1 whereinsaid cutting means includes a blade holder having a blade supportingface, means for clamping a cutting blade to said face, and a part towhich pressure may be applied to pivot said cutting means.
 3. A cuttingblock of the type described in claim 2 wherein said part to whichpressure may be applied is positioned so that pressure applied to saidpart after the cutting means has engaged a sheet is operative to movethe block along the guide in the direction of the pressure.
 4. A cutTingblock of the type described in claim 2 wherein said blade supportingface is at a non-perpendicular angle to said board whereby said cuttingmeans makes bevel cuts in a sheet.
 5. A cutting block of the typedescribed in claim 4 wherein the pivoting of said cutting means causesit to engage a sheet at an angle; and wherein the angle at which saidcutting means engages a sheet is equal to said non-perpendicular angle.6. A cutting block of the type described in claim 5 wherein saidnon-perpendicular angle is 60*.
 7. A cutting block of the type describedin claim 2 wherein said scale is positioned parallel to said bladesupporting face and is spaced therefrom by a distance slightly greaterthan the thickness of a cutting blade, whereby a blade positionedbetween the face and the scale is held against lateral movement.
 8. Acutting block of the type described in claim 1 wherein said cuttingmeans is supported at a non-perpendicular angle to said board wherebybevel cuts may be made in a sheet.
 9. A cutting block of the typedescribed in claim 1 wherein said scale extends in both directions fromsaid reference marking.
 10. A cutting block of the type described inclaim 9 wherein there are a pair of said reference markings, one foreach direction in which said scale extends, said reference markingsbeing slightly separated to compensate for the width of the blade.
 11. Acutting block of the type described in claim 1 including at least onescallop in said scale in the area of said reference marking to providemaximum visibility of the blade in that area.
 12. A sheet materialcutting device comprising: a cutting board; a guide extending over thetop of the board; a cutting block mounted for sliding movement alongsaid guide, said cutting block including a cutting means normally biasedaway from said board but adapted to be moved toward the board intoengagement with a sheet position thereon; and a scale mounted formovement with said block, said scale having a reference marking at thepoint where said cutting means engages a sheet and extending from saidreference marking in at least one direction, said scale being graduatedin units of linear measurement starting at said reference marking andbeing adapted to be directly indexed on an edge of said sheet material,whereby the points at which the beginning and end of a cut occur may beeasily and accurately observed.
 13. A device of the type described inclaim 12 wherein said scale extends in both directions from saidreference marking.
 14. A device of the type described in claim 12including a stationary scale positioned on top of said board andextending from near one end of said guide in a direction perpendicularthereto.
 15. A device of the type described in claim 14 wherein saidstationary scale extends in both directions from said guide.
 16. Adevice of the type described in claim 12 including means for supportingsaid guide to prevent lateral movement thereof.
 17. A device of the typedescribed in claim 16 wherein said means for supporting is a bracketmounted to permit a large sheet to pass thereunder.
 18. A mat cuttingdevice comprising: a cutting board adapted to have a mat positionedthereon; a guide extending over the top of the board; a cutting blockmounted for sliding movement along said guide, said cutting blockincluding a cutting means mounted at a non-perpendicular angle to theboard, said cutting means being normally biased away from said board butbeing adapted to be pivoted into angular engagement with a mat positionon said board and to be moved with said block along said guide to make abevel cut in said mat; and a scale mounted for movement with said block,said scale having a reference marking at the point where said cuttingmeans engages a mat when pivoted and extending from said referencemarking in at least one direction, said scale being graduated in unitsof linear measurement starting at said reference marking anD beingadapted to be directly indexed on an edge of said sheet material,whereby the points at which the beginning and end of a cut occur may beeasily and accurately observed.
 19. A mat cutting device of the typedescribed in claim 18 wherein the angle at which said cutting means ispivoted into engagement with said mat is equal to said non-perpendicularangle.